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An example of a set that is closed under addition is the set of all integers, denoted as (\mathbb{Z}). This means that if you take any two integers and add them together, the result will also be an integer. For instance, adding 3 and -5 results in -2, which is still an integer. Thus, (\mathbb{Z}) satisfies the property of closure under addition.
What else can I help you with?
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Are all integers closed under addition?
Yes, all integers are closed under addition. This means that when you add any two integers together, the result is always another integer. For example, adding -3 and 5 yields 2, which is also an integer. Therefore, the set of integers is closed under the operation of addition.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Are integers closed under addition?
yes
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
Are real numbers closed under addition?
yes because real numbers are any number ever made and they can be closed under addition
ARe odd integers not closed under addition?
That is correct, the set is not closed.
Is the set of real numbers closed under addition?
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Are integers closed under addition?
yes
Are rational numbers closed under division multiplication addition or subtraction?
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
Are the set of rational numbers closed under addition?
Yes, the set is closed.
